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      <H1>Poisson regression with spatially correlated random effects 
      <BR></H1></DIV><BR><BR></TD></TR>
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          <TD align=middle><FONT face="Arial, Helvetica" color=white><B>ADMB 
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                <TD>Code: <A 
                  href="spatial.tpl">spatial.tpl</A><BR>Data: 
                  <A 
                  href="spatial.dat">spatial.dat</A><BR>Initial 
                  values: <A 
                  href="spatial.pin">spatial.pin</A>
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Expected Results: 
                  <A 
                  href="spatial-expected-results.par">spatial.par</A><BR><BR></FONT></TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE><BR>
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                <TD>In a <A 
                  href="http://otter-rsch.com/admbre/examples/admb_tutorial.html">DOS</A> 
                  window<BR>Under <A 
                  href="http://otter-rsch.com/admbre/examples/admb_tutorial.html">linux</A><BR></TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE><BR>
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          <TD align=middle><FONT face="Arial, Helvetica" 
            color=white><B>Results: Computation times</B></FONT> </TD></TR>
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                <TD>ADMB-RE: 22 
      seconds<BR></TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE><BR>
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      <H3><STRONG>Model description</STRONG></H3>Our data 
      <EM>y<SUB>i,j</SUB></EM> are observed on a regular 10x10 grid of points: 
      {<EM>i,j</EM>=1,...,10}. It is assumed that <EM>y<SUB>i,j</SUB></EM> ~ 
      Poisson(<FONT face=Symbol>l</FONT><SUB><EM>i,j</EM></SUB>), where <BR><BR>
      <DIV align=center>log(<FONT face=Symbol>l</FONT><SUB>i,j</SUB>) = 
      X<SUB><EM>i,j</EM></SUB><FONT face=Symbol>b</FONT> + <FONT 
      face=Symbol>e</FONT><SUB><EM>i,j</EM></SUB>. </DIV><BR>Here, 
      <EM>X<SUB>i,j</SUB></EM><FONT face=Symbol>b</FONT> is a linear predictor 
      and <FONT face=Symbol>e</FONT><SUB>i,j</SUB> are Gaussian random variables 
      with covariance <BR>
      <DIV align=center>cov(<FONT 
      face=Symbol>e</FONT><SUB><EM>i1,j1</EM></SUB>,<FONT 
      face=Symbol>e</FONT><SUB><EM>i2,j2</EM></SUB>) = <FONT 
      face=Symbol>s</FONT><SUP>2</SUP> exp(<FONT 
      face=Symbol>a</FONT><SUP>-1</SUP> <EM>d</EM>), </DIV><BR><BR>where 
      <EM>d</EM> is the Euclidean distance. 

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